Keldysh

Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya Square 4,125047 Moscow, Russia e-mail kuchanov orc.ru... 

Since the non-tilde operators describe physical variables, G(k (3)11 is the physical propagator to be used to treat the properties of the thermal bosonic system. It is interesting to observe that, except for the non-diagonal elements, this TFD-propagator is equal to the one introduced in the Schwinger-Keldysh approach, which is claimed to be (in this equivalence with TFD) a thermal theory describing linear-response processes only (H. Chu et.al., 1994). 

To describe nonequilibrium phase transitions, there have been developed many methods such as the closed-time path integral by Schwinger and Keldysh (J. Schwinger et.al., 1961), the Hartree-Fock or mean field method (A. Ringwald, 1987), and the l/lV-expansion method (F. Cooper et.al., 1997 2000). In this talk, we shall employ the so-called Liouville-von Neumann (LvN) method to describe nonequilibrium phase transitions (S.P. Kim et.al., 2000 2002 2001 S.P. Kim et.al., 2003). The LvN method is a canonical method that first finds invariant operators for the quantum LvN equation and then solves exactly the... 

The effect of thermal pion fluctuations on the specific heat and the neutrino emissivity of neutron stars was discussed in [27, 28] together with other in-medium effects, see also reviews [29, 30], Neutron pair breaking and formation (PBF) neutrino process on the neutral current was studied in [31, 32] for the hadron matter. Also ref. [32] added the proton PBF process in the hadron matter and correlation processes, and ref. [33] included quark PBF processes in quark matter. PBF processes were studied by two different methods with the help of Bogolubov transformation for the fermion wave function [31, 33] and within Schwinger-Kadanoff-Baym-Keldysh formalism for nonequilibrium normal and anomalous fermion Green functions [32, 28, 29],... 

In this section, we describe our model, and give a brief, self-contained account on the equations of the non-equilibrium Green function formalism. This is closely related to the electron and particle-hole propagators, which have been at the heart of Jens electronic structure research [7,8]. For more detailed and more general analysis, see some of the many excellent references [9-15]. We restrict ourselves to the study of stationary transport, and work in energy representation. We assume the existence of a well-defined self-energy. The aim is to solve the Dyson and the Keldysh equations for the electronic Green functions ... 

Keldysh and Kopaev 1965, Kohn 1967, Halperin and Rice 1968a, b).f However, it appears that when the surfaces are anisotropic (Brinkman and Rice 1973) and correlation is included (Vashishta et al. 1973), the reverse is usually the case. 

In 1958, Franz [45] and Keldysh [46] independently theoretically predicted the absorption by a semiconductor, placed in an electric field, of light quanta which have an energy less than the width of the forbidden gap. The effect is connected with interband tunneling (Fig. 20). The valence band electron tunnels from point xl to point 3c, then it absorbs a quantum with a frequency lo < Eg (Eg is the width of the forbidden gap) and further tunnels to point x2. Using the law of conservation of energy and the law of conservation of imaginary momentum (see the previous section), it is easy to show that light absorption at point 3c, which lies exactly between points acj and x2, is optimal. Consequently... 

Experimental observation of the Franz Keldysh effect in real semiconductors is complicated by the possibility of absorption at u) < Eg in the absence of an electric field. This absorption can result from various phenomena including exciton excitations, the influence of impurities on the... 

The Editors feel that they should note other positive responses by mathematicians to Ya.B. s book as well. In 1968 the RSFSR Ministry of Education, on the recommendation of the Scientific Council of the AS USSR Institute of Applied Mathematics chaired by M. V. Keldysh, recommended the book Higher Mathematics for Beginners and its Applications to Physics as a textbook for physico-mathematical schools and elective study. A very prominent American mathematician, Lippman Bers, wrote, Finally, I would like to indicate how I was influenced by two very nonstandard books on mathematical analysis a historical survey written by the outstanding mathematician O. Toeplitz, and a textbook written by a well-known physicist, Ya. Zeldovich (unfortunately not yet available to the British or American reader). ... 

One can study the spin dynamics integrating out the environment and using the effective action for the spin. We derive the effective action using the Feynman-Vernon-Keldysh technique. For the interaction —Xsz with the z-component of the spin, the effective action (the influence functional) reads... 

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